A solid wood door $1\mathrm{.}0$m wide and $2\mathrm{.}0$m high is hinged at one side and has a total

mass of $40\mathrm{.}0$kg$.$ Initially open and at rest, the door is struck at its center by a

handful of $($sticky$)$ mud with a mass of $0\mathrm{.}5$kg$.$ traveling perpendicular to the door

at $12\mathrm{.}0$m$/$s just before impact.

a$.$ What is the final angular speed of the door?

b$.$ Does the mud make a significant contribution to the moment of inertia?